AUGUSTA, Maine — Democrats who’ve wrested control of the Legislature back from Republicans are poised to reverse a GOP health insurance overhaul when the 2013 session gets going.

The law, passed in 2011 after Republicans pushed for years for the changes, seeks to lower health insurance costs and cover more Maine residents through a series of market changes. It adds a $4 charge to the monthly premium of every Mainer with private coverage to pay for a new pool of high-risk people with the highest health care expenses. The law also allows Maine residents to buy coverage offered in other states.

The bill rankled Democrats as it was being debated. Then the minority, Democrats claimed the far-reaching law was not sufficiently deliberated and was “rammed through” the legislative process.

Now back at the reins, Democrats have toned down their rhetoric and spoken mostly in general terms about their legislative intentions for the year. But on one topic — the health insurance overhaul — they’ve been specific.

“We just talked to 600,000 Mainers, and a lot of them were very frustrated by the premium increases that they’re facing,” said the new Democratic Senate president, Justin Alfond, referring to the Nov. 6 election.

“And so we absolutely are going to go back to the drawing board and looking at the places where that bill didn’t meet its goal. And we’re going to go to our Republican colleagues and say, ‘What do you think about these possible changes and tweaks?’ And then we’re going to have to work with the governor, too,” said Alfond, of Portland.

In one of his earliest statements after winning Democrats’ nomination for House speaker, Rep. Mark Eves also declared that the law would be on the table.

“I think the Republican insurance bill is one that has been really hard on a lot of people, particularly in rural Maine, and middle-aged Mainers,” said Eves, of North Berwick. “So we’re going to look at that again.”

The new Republican House minority leader, Ken Fredette of Newport, said, when asked if his party considered the insurance reforms untouchable: “Any piece of legislation is something we need to be able to look at it and have an adult conversation and say, ‘Is there a way to possibly improve this legislation?”’

“I don’t think anyone believes that any particular law is perfect; there’s always ways to improve it. If there are ways to improve it, we certainly can reach across the aisle and do that,” Fredette said.

The 2011 insurance overhaul isn’t the only health care issue likely to come up during the 2013 session, which formally starts Dec. 5 but won’t get under way in earnest until early January.

And in some ways, the issue has already triggered debate. Republican Gov. Paul LePage, who opposes the national Affordable Care Act, has declared that Maine will do nothing to comply with that law’s requirement that states must set up health care exchanges unless they want the federal government to come in and do it instead. That makes it more likely Maine will have to go with the latter alternative for an exchange, an online site where individuals and businesses can shop for insurance.

The back-and-forth has already begun on another issue related to the national health care law: expansion of Medicaid so it covers more uninsured people.

While the U.S. Supreme Court has ruled that the states can’t be forced to expand Medicaid, Democrats assert that Maine would lose millions of dollars in federal subsidies for the health care programs and that refusing the money would in effect be giving it away to other states.

Democrats also say that the federal subsidies make good financial sense for the states. That’s because the federal government will pay 100 percent of the cost to insure new Medicaid enrollees who meet eligibility standards. That payment continues for three years beginning in 2014, and the federal government’s share will gradually decrease to 90 percent in 2020.

LePage, however, has taken a firm stand against expanded Medicaid coverage, which was cut back in several areas in Maine’s last budget. The governor says the costs exceed the state’s ability to pay and must be curtailed.